The New Science of (Random) Networks

The New Science of (Random) Networks

FEBRUARY 2004 | Rick Durrett
The article reviews two books on network science: "Linked: The New Science of Networks" by Albert-László Barabási and "Six Degrees: The Science of a Connected Age" by Duncan J. Watts. Both books explore the underlying order and rules governing various networks, from social interactions to technological systems, and their implications for fields such as economics, epidemiology, and business. Barabási's book is characterized by its confident and sometimes hyperbolic tone, making far-reaching conclusions based on simulation and database analysis. It includes anecdotes and historical context, such as the work of Erdős and Renyi on random graphs and Milgram's six degrees of separation experiment. The book is praised for its accessibility but criticized for its lack of mathematical rigor. Watts's book takes a more modest and detailed approach, focusing on the development of the small-world model and the beta model, which introduce the concept of scale-free networks. The book provides background information and relates network science to contemporary social science, making it more appealing to mathematicians and social scientists. Both books are engaging but lack a deep mathematical treatment, which the reviewer suggests readers interested in the mathematical underpinnings should refer to Mark Newman's article in *SIAM Review*. The review also discusses the significance of power law distributions in network degrees, the differences between Erdős-Renyi and scale-free networks, and the implications of these differences for processes like epidemic spread and network reliability.The article reviews two books on network science: "Linked: The New Science of Networks" by Albert-László Barabási and "Six Degrees: The Science of a Connected Age" by Duncan J. Watts. Both books explore the underlying order and rules governing various networks, from social interactions to technological systems, and their implications for fields such as economics, epidemiology, and business. Barabási's book is characterized by its confident and sometimes hyperbolic tone, making far-reaching conclusions based on simulation and database analysis. It includes anecdotes and historical context, such as the work of Erdős and Renyi on random graphs and Milgram's six degrees of separation experiment. The book is praised for its accessibility but criticized for its lack of mathematical rigor. Watts's book takes a more modest and detailed approach, focusing on the development of the small-world model and the beta model, which introduce the concept of scale-free networks. The book provides background information and relates network science to contemporary social science, making it more appealing to mathematicians and social scientists. Both books are engaging but lack a deep mathematical treatment, which the reviewer suggests readers interested in the mathematical underpinnings should refer to Mark Newman's article in *SIAM Review*. The review also discusses the significance of power law distributions in network degrees, the differences between Erdős-Renyi and scale-free networks, and the implications of these differences for processes like epidemic spread and network reliability.
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